A stress at an arbitrary point on or in an elastic body is generally expressed in terms of six components .sigma..sub.x, .sigma..sub.y, .sigma..sub.z, .tau..sub.xy, .tau..sub.yz and .tau..sub.zx when the (x, y, z) rectangular Cartesian coordinate system is used. Among them, .sigma..sub.x, .sigma..sub.y, .sigma..sub.z are normal stress components acting on planes vertical to the x-, y- and z-axes, respectively. .tau..sub.xy is a shearing stress acting on a plane with x=constant in the direction of the y-axis and on a plane with y=constant in the direction of the x-axis. Also, .tau..sub.yz and .tau..sub.zx are shearing stresses. All the subscripts obey the same definition. With respect to this point, if an appropriate system of coordinates is selected, all the shearing stress components are vanished, and only the normal stress components exist. These normal stress components are known as principal stresses .sigma..sub.1, .sigma..sub.2 and .sigma..sub.3, respectively.
If a stress change is adiabatically applied to an elastic body, a temperature change occurs proportionately. This phenomenon is known as the thermoelastic effect and was discovered by Weber, Kelvin, and other in the 19th century. Let .DELTA.T be the temperature difference produced before and after application of a stress by the thermoplastic effect. We have the relation EQU .DELTA.T=-KT(.sigma..sub.1 +.sigma..sub.2 +.sigma..sub.3)
where K is a thermoelastic constant intrinsic to the material and T is absolute temperature. The sum of the principal stresses (.sigma..sub.1 +.sigma..sub.2 +.sigma..sub.3) is the stress invariant of the first order. The theory of elasticity has demonstrated that this sum of the principal stresses is equal to (.sigma..sub.x +.sigma..sub.y +.sigma..sub.z), irrespective of how the system of coordinates (x, y, z) is determined. The temperature difference .DELTA.T is in proportion to the sum of the principal stresses because the volume change of the elastic body following Hooke's Law is determined by the stress invariant of the first order and because the volume of the elastic body is varied by none of the shearing stress components .tau..sub.xy, .tau..sub.yz and .tau..sub.zx.
We have already proposed methods of easily measuring stress distributions by making use of the above-described thermoelastic effect, as described, for example, in Japanese Patent Publication Nos. 1204/1987, 1205/1987 and 7333/1988. In particular, compressive and tensile loads are repeatedly applied to an elastic body by utilizing the thermoelastic effect. The resulting temperature variation pattern on the surface of the elastic body is detected by an infrared camera. Thus, the distribution of the stress invariant of the first order is measured.
On the other hand, known methods for numerically analyzing the stress distribution on and in an elastic body include the finite element method, the boundary element method and the calculus of finite differences. In these methods, a model having the same shape as an actual object is prepared. Elastic constants and applied external forces are given as boundary conditions to the model. The stress distribution in and on the elastic body is found. proportion to the distribution of the stress invariant of the first order, i.e., the sums of the principal stresses (.sigma..sub.1 +.sigma..sub.2 +.sigma..sub.3) as mentioned previously. However, it is impossible to know the individual stress components .sigma..sub.x, .sigma..sub.y, .sigma..sub.z, .tau..sub.xy, .tau..sub.yz and .tau..sub.zx only from the temperature variation pattern. On the other hand, in methods of numerical stress analysis such as the finite element method, it is not easy to set the boundary conditions appropriately. Therefore, it is not assured that the obtained results correspond to the stress distribution on and in the actual object.